Advertisements
Advertisements
Question
Solve the following equation by factorization
`4sqrt(3)x^2 + 5x - 2sqrt(3)` = 0
Advertisements
Solution
`4sqrt(3)x^2 + 5x - 2sqrt(3)` = 0
`{4sqrt(3) xx (-2sqrt(3)) = 8xx (-3) = -24}`
`4sqrt(3)x^2 + 8x - 3x - 2sqrt(3)` = 0
⇒ `4x (sqrt(3)x + 2) - sqrt(3)(sqrt(3)x + 2)` = 0
⇒ `(sqrt(3)x + 2) (4x - sqrt(3))` = 0
Either `sqrt(3)x + 2` = 0,
then `sqrt(3)x` = -2
⇒ x = `-(2)/sqrt(3)`
⇒ x = `(-2 xx sqrt(3))/(sqrt(3) xx sqrt(3))`
= `(-2sqrt(3))/(3)`
or
`4x - sqrt(3)` = 0,
then `4x = sqrt(3)`
⇒ x = `sqrt(3)/(4)`
Hence x = `(-2sqrt(3))/(3), sqrt(3)/(4)`.
APPEARS IN
RELATED QUESTIONS
Solve the equation `4/x-3=5/(2x+3); xne0,-3/2` for x .
Solve (i) x2 + 3x – 18 = 0
(ii) (x – 4) (5x + 2) = 0
(iii) 2x2 + ax – a2 = 0; where ‘a’ is a real number
Solve the following quadratic equations by factorization:
`2/2^2-5/x+2=0`
Solve the following quadratic equations by factorization:
`x^2-(sqrt3+1)x+sqrt3=0`
Solve 2x2 – 9x + 10 =0; when x ∈ Q
Solve the given quadratic equation for x : 9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0 ?
Solve the following quadratic equations by factorization: \[\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 4 - \frac{2x + 3}{x - 2}; x \neq 1, - 2, 2\]
Solve the following quadratic equation by factorization method : `"x"^2 - 5"x" - 36 = 0`
In each of the following determine whether the given values are solutions of the equation or not.
x2 + x + 1 = 0; x = 1, x = -1.
The length of a rectangular garden is 12 m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden.
